You sit down with a well mixed deck containing A cards marked "+" and B cards marked "—". You may draw cards from this deck as long as you want, i.e., you can stop playing at any point. Each time you draw a + card you are given $1 and each time you draw a — card you have to pay $1. Cards are not replaced after having been drawn.

What would be a fair amount to pay for the right to play (i.e., what is the expected payoff) and under what circumstance should a player cease drawing?

Only ed bottemiller continues to believe one should refuse to play or stop playing when there is an equality in the number of + and - cards remaining. I initally thought that, but leming corrected me. My extended table below,

shows that if there is 1 +, play should stop if there are 2 or more -'s. If there are 2 +'s, stop if there are 4 or more -'s (where the zeros begin in the expected values). If there are 3 +'s, stop if there are 5 or more -'s. If there are 4 +'s stop if there are 7 or more -'s.

The table is of course recursive, rather than closed-form, but does give the expected value for a given A and B, such as 8.32 when A=12 and B=4.